Question

A particle moves under the effect of a force $F=cx\ from\ x=0\ to\ x=x_{1}$, the work done in the process is
(a) $cx_{1}^{2}$
(b) $\frac{1}{2}cx_{1}^{2}$
(c) $2cx_{1}^{2}$
(d) zero

Answer 1

Pta nii sorry.. Google

Answer 2

The force is dependent on the position of the particle. Thus, we need to find  the work done on the particle for a small displacement. The network is carried out by the force over the displacement from x = 0 to x = x1

Thus, F = cx

For a small displacement dx the work done on the particle is

dW=Fdx= (cx)dx

The work done in moving the particle from x = 0 to x = x1 is given as -

W = ∫dW = x-x1∫x-0 c(x)dx

W = cx-x1∫x-0 xdx = c[x²/s]

W = c [ x1²/2-0²/2]

W = c.x1²/2

W = 1/2cx1²

Therefore the work done in the process is - 1/2cx1²